Details

Time bar (total: 19.4s)

sample167.0ms

Algorithm
intervals
Results
76.0ms82×body1280valid
27.0ms74×body640valid
24.0ms268×body80valid
11.0ms39×body320valid
3.0ms16×body160valid

simplify158.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
01219
12513
24913
37613
49513
511113
612513
713913
done13913

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.7b

localize17.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* a1 a1) (* a2 a2))
0.6b
(* (/ (cos th) (sqrt 2.0)) (+ (* a1 a1) (* a2 a2)))
0.7b
(/ (cos th) (sqrt 2.0))

rewrite96.0ms

Algorithm
rewrite-expression-head
Rules
40×add-sqr-sqrt
38×times-frac
32×add-cube-cbrt *-un-lft-identity
22×associate-*l* sqrt-prod
10×add-exp-log add-cbrt-cube
6×associate-/r*
5×pow1 add-log-exp
3×flip3-+ associate-*r* flip-+ associate-/l* unswap-sqr
2×cbrt-undiv frac-times associate-*r/ div-exp prod-exp cbrt-unprod div-inv
1×+-commutative distribute-rgt-in frac-2neg distribute-lft-in pow-prod-down associate-*l/ clear-num sum-log *-commutative
Counts
3 → 98
Calls
3 calls:
8.0ms
(+ (* a1 a1) (* a2 a2))
62.0ms
(* (/ (cos th) (sqrt 2.0)) (+ (* a1 a1) (* a2 a2)))
20.0ms
(/ (cos th) (sqrt 2.0))

series419.0ms

Counts
3 → 9
Calls
3 calls:
30.0ms
(+ (* a1 a1) (* a2 a2))
284.0ms
(* (/ (cos th) (sqrt 2.0)) (+ (* a1 a1) (* a2 a2)))
105.0ms
(/ (cos th) (sqrt 2.0))

simplify1.6s

Counts
107 → 107
Iterations

Useful iterations: done (1.6s)

IterNodesCost
01581536
14801469
215991325
done50001322

prune448.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.3b

localize22.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* a1 a1) (* a2 a2))
0.4b
(* (cos th) (+ (* a1 a1) (* a2 a2)))
0.4b
(/ (* (cos th) (+ (* a1 a1) (* a2 a2))) (sqrt 2.0))

rewrite71.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
10×add-exp-log add-cbrt-cube
9×add-cube-cbrt *-un-lft-identity
6×times-frac associate-/r* sqrt-prod
5×pow1 add-log-exp
4×associate-*r/
3×flip3-+ associate-*r* associate-*l* flip-+
2×cbrt-undiv div-exp prod-exp cbrt-unprod associate-/l/
1×+-commutative distribute-rgt-in frac-2neg distribute-lft-in pow-prod-down clear-num sum-log *-commutative div-inv associate-/l* unswap-sqr
Counts
3 → 62
Calls
3 calls:
9.0ms
(+ (* a1 a1) (* a2 a2))
32.0ms
(* (cos th) (+ (* a1 a1) (* a2 a2)))
26.0ms
(/ (* (cos th) (+ (* a1 a1) (* a2 a2))) (sqrt 2.0))

series502.0ms

Counts
3 → 9
Calls
3 calls:
34.0ms
(+ (* a1 a1) (* a2 a2))
146.0ms
(* (cos th) (+ (* a1 a1) (* a2 a2)))
321.0ms
(/ (* (cos th) (+ (* a1 a1) (* a2 a2))) (sqrt 2.0))

simplify1.6s

Counts
71 → 71
Iterations

Useful iterations: 2 (240.0ms)

IterNodesCost
01151083
13031038
21190886
done5000886

prune288.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.3b

localize39.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* (cos th) (sqrt (+ (* a1 a1) (* a2 a2)))) (sqrt (+ (* a1 a1) (* a2 a2))))
0.4b
(/ (* (* (cos th) (sqrt (+ (* a1 a1) (* a2 a2)))) (sqrt (+ (* a1 a1) (* a2 a2)))) (sqrt 2.0))
7.3b
(sqrt (+ (* a1 a1) (* a2 a2)))
7.3b
(sqrt (+ (* a1 a1) (* a2 a2)))

rewrite288.0ms

Algorithm
rewrite-expression-head
Rules
28×sqrt-div
18×add-exp-log add-cbrt-cube
16×associate-*r/
15×sqrt-prod
14×add-sqr-sqrt flip3-+ flip-+
12×add-cube-cbrt *-un-lft-identity
11×pow1
8×frac-times associate-/l/
6×times-frac associate-*r* prod-exp associate-/r* cbrt-unprod
4×associate-*l/ add-log-exp
3×cbrt-undiv div-exp pow-prod-down
2×rem-sqrt-square sqrt-pow1 pow1/2
1×frac-2neg associate-*l* clear-num *-commutative div-inv associate-/l*
Counts
4 → 96
Calls
4 calls:
130.0ms
(* (* (cos th) (sqrt (+ (* a1 a1) (* a2 a2)))) (sqrt (+ (* a1 a1) (* a2 a2))))
121.0ms
(/ (* (* (cos th) (sqrt (+ (* a1 a1) (* a2 a2)))) (sqrt (+ (* a1 a1) (* a2 a2)))) (sqrt 2.0))
16.0ms
(sqrt (+ (* a1 a1) (* a2 a2)))
17.0ms
(sqrt (+ (* a1 a1) (* a2 a2)))

series605.0ms

Counts
4 → 12
Calls
4 calls:
173.0ms
(* (* (cos th) (sqrt (+ (* a1 a1) (* a2 a2)))) (sqrt (+ (* a1 a1) (* a2 a2))))
323.0ms
(/ (* (* (cos th) (sqrt (+ (* a1 a1) (* a2 a2)))) (sqrt (+ (* a1 a1) (* a2 a2)))) (sqrt 2.0))
52.0ms
(sqrt (+ (* a1 a1) (* a2 a2)))
57.0ms
(sqrt (+ (* a1 a1) (* a2 a2)))

simplify1.9s

Counts
108 → 108
Iterations

Useful iterations: 2 (205.0ms)

IterNodesCost
01432565
13611886
212881526
done50001526

prune575.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.3b

localize36.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (sqrt (+ (* a1 a1) (* a2 a2))) (cbrt (sqrt 2.0)))
0.3b
(* (/ (* (cos th) (sqrt (+ (* a1 a1) (* a2 a2)))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (/ (sqrt (+ (* a1 a1) (* a2 a2))) (cbrt (sqrt 2.0))))
7.3b
(sqrt (+ (* a1 a1) (* a2 a2)))
7.3b
(sqrt (+ (* a1 a1) (* a2 a2)))

rewrite181.0ms

Algorithm
rewrite-expression-head
Rules
115×times-frac
107×add-sqr-sqrt sqrt-prod
85×add-cube-cbrt *-un-lft-identity
82×cbrt-prod
58×associate-*r*
47×add-exp-log
33×add-cbrt-cube
18×prod-exp cbrt-unprod
14×cbrt-undiv div-exp
9×associate-/r*
8×pow1
7×unswap-sqr
6×sqrt-div associate-/l*
5×associate-*l*
4×add-log-exp
3×flip3-+ flip-+ div-inv
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-/l/
1×frac-times frac-2neg associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative
Counts
4 → 215
Calls
4 calls:
22.0ms
(/ (sqrt (+ (* a1 a1) (* a2 a2))) (cbrt (sqrt 2.0)))
123.0ms
(* (/ (* (cos th) (sqrt (+ (* a1 a1) (* a2 a2)))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (/ (sqrt (+ (* a1 a1) (* a2 a2))) (cbrt (sqrt 2.0))))
8.0ms
(sqrt (+ (* a1 a1) (* a2 a2)))
13.0ms
(sqrt (+ (* a1 a1) (* a2 a2)))

series764.0ms

Counts
4 → 12
Calls
4 calls:
371.0ms
(/ (sqrt (+ (* a1 a1) (* a2 a2))) (cbrt (sqrt 2.0)))
282.0ms
(* (/ (* (cos th) (sqrt (+ (* a1 a1) (* a2 a2)))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (/ (sqrt (+ (* a1 a1) (* a2 a2))) (cbrt (sqrt 2.0))))
51.0ms
(sqrt (+ (* a1 a1) (* a2 a2)))
61.0ms
(sqrt (+ (* a1 a1) (* a2 a2)))

simplify2.0s

Counts
227 → 227
Iterations

Useful iterations: done (2.0s)

IterNodesCost
02676832
17095948
230635248
done50005057

prune992.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.3b

regimes315.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify7.0ms

Iterations

Useful iterations: done (7.0ms)

IterNodesCost
01936
12534
done2532

end0.0ms

sample6.2s

Algorithm
intervals
Results
2.1s8073×body80valid
2.0s2498×body1280valid
947.0ms1995×body640valid
476.0ms1075×body320valid
151.0ms529×body160valid